Absolute distance meter that measures a moving retroreflector

CROSS REFERENCE TO RELATED APPLICATIONS

0001This application claims priority to U.S. provisional application, 60/614,778, filed Sep. 30, 2004, the entire contents of which are hereby incorporated by reference.

BACKGROUND

0002The present disclosure relates to a coordinate measuring device. One set of coordinate measurement devices belongs to a class of instruments that measure the coordinates of a point by sending a laser beam to the point. The laser beam may impinge directly on the point or may impinge on a retroreflector target that is in contact with the point. In either case, the instrument determines the coordinates of the point by measuring the distance and the two angles to the target. The distance is measured with a distance-measuring device such as an absolute distance meter or an interferometer. The angles are measured with an angle-measuring device such as an angular encoder. A gimbaled beam-steering mechanism within the instrument directs the laser beam to the point of interest. Exemplary systems for determining coordinates of a point are described by U.S. Pat. No. 4,790,651 to Brown et al. and U.S. Pat. No. 4,714,339 to Lau et al.

0003The laser tracker is a particular type of coordinate-measuring device that tracks the retroreflector target with one or more laser beams it emits. A device that is closely related to the laser tracker is the laser scanner. The laser scanner steps one or more laser beams to points on a diffuse surface. The laser tracker and laser scanner are both coordinate-measuring devices. It is common practice today to use the term laser tracker to also refer to laser scanner devices having distance- and angle-measuring capability. This broad definition of laser tracker, which includes laser scanners, is used throughout this application.

0004One type of laser tracker contains only an interferometer without an absolute distance meter. If an object blocks the path of the laser beam from one of these trackers, the interferometer loses its distance reference. The operator must then track the retroreflector to a known location before continuing the measurement. A way around this limitation is to put an absolute distance meter (ADM) in the tracker. The ADM can measure distance in a point-and-shoot manner. Some laser trackers contain only an ADM without an interferometer. An exemplary laser tracker of this type is described in U.S. Pat. No. 5,455,670 to Payne, et al. Other laser trackers typically contain both an ADM and an interferometer. An exemplary laser tracker of this type is described in U.S. Pat. No. 5,764,360 to Meier, et al.

0005One of the main applications for laser trackers is to scan the surface features of objects to determine their geometrical characteristics. For example, an operator can determine the angle between two surfaces by scanning each of the surfaces and then fitting a geometrical plane to each. As another example, an operator can determine the center and radius of a sphere by scanning the sphere surface. Up until this time, an interferometer, rather than an ADM, has been required for the laser tracker to scan. The reason for this is that absolute distance measurements have only been possible on stationary targets. Consequently, to get full functionality with both scanning and point-and-shoot capability, laser trackers have required both an interferometer and an ADM. What is needed is an ADM that has the ability to accurately and quickly scan a moving target. This permits tracker cost to be reduced because the interferometer is no longer needed.

SUMMARY

0006The above and other problems and disadvantages of the prior art are overcome and alleviated by embodiments the present laser device, which utilizes an absolute distance meter to determine the distance to a moving retroreflector.

0007A laser device and method is disclosed capable of one or more dimensional absolute distance measurements and/or surface scanning and/or coordinate measurements of a moving external retroreflector or other moving target surfaces without using an incremental interferometer depending upon what the application requires.

0008The above-discussed and other features and advantages of the present apparatus and method will be appreciated and understood by those skilled in the art from the following detailed description and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

0009Referring now to the drawings, wherein like elements are numbered alike in the several FIGURES:

0010<figref idref="DRAWINGS">FIG. 1</figref> is a perspective view of an exemplary laser tracker sending a laser beam to an external retroreflector; and

0011<figref idref="DRAWINGS">FIG. 2</figref> is a block diagram of some of the main elements within the exemplary laser tracker of <figref idref="DRAWINGS">FIG. 1</figref>; and

0012<figref idref="DRAWINGS">FIG. 3</figref> is a block diagram of the elements within the exemplary fiber-coupling network of <figref idref="DRAWINGS">FIG. 2</figref>; and

0013<figref idref="DRAWINGS">FIG. 4</figref> is a block diagram of the elements within the exemplary ADM electronics of <figref idref="DRAWINGS">FIG. 2</figref>; and

0014<figref idref="DRAWINGS">FIG. 5</figref> is a block diagram of the elements within an exemplary ADM data-processing system for computing the distance to a moving retroreflector.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

0015Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings.

0016An exemplary laser tracker <b>10</b> is illustrated in <figref idref="DRAWINGS">FIG. 1</figref>. An exemplary gimbaled beam-steering mechanism <b>12</b> of the laser tracker comprises zenith carriage <b>14</b> that is mounted on azimuth base <b>16</b>. The zenith and azimuth mechanical axes internal to the tracker (not shown) are turned to point the laser beam <b>46</b> in the desired direction. The laser beam may comprise one or more laser wavelengths, as will be described in the discussion that follows. The zenith and azimuth angular encoders internal to the tracker (not shown) are attached to the zenith and azimuth mechanical axes and indicate, to high accuracy, the angles of rotation. For the sake of clarity and simplicity, this sort of gimbal mechanism <b>12</b> is assumed in the following discussion. However, other types of gimbal mechanisms are possible, and the techniques described here are also applicable to these other types.

0017Laser beam <b>46</b> travels to external retroreflector <b>26</b>. The most common type of retroreflector is a spherically mounted retroreflector (SMR), which comprises a metal sphere into which a cube-corner retroreflector (not shown) is embedded. The cube-corner retroreflector comprises three perpendicular mirrors that come together at a common apex point. The apex point is placed at the center of the metal sphere. Instead of an SMR, a retrosphere or any other device that sends the return laser beam back on itself may be used as the external retroreflector <b>26</b>.

0000Elements of the Laser Tracker

0018Some of the main elements within the laser tracker are shown in <figref idref="DRAWINGS">FIG. 2</figref>. ADM electronics <b>300</b> modulates the optical power of ADM laser <b>102</b>, which sends light through fiber-optic cable <b>104</b> and fiber-coupling network <b>200</b>. Some of the light from the fiber-coupling network <b>200</b> travels to ADM beam launch <b>140</b>. Another part of the light travels through fiber loop <b>106</b> and then back into fiber-coupling network <b>200</b>. ADM beam launch <b>140</b> comprises stable ferrule <b>142</b> and positive lens <b>144</b>. Collimated light <b>108</b> emerges from the fiber launch <b>140</b>.

0019In the event that the ADM laser operates at an infrared wavelength, it is convenient to provide a visible laser beam to help make the ADM beam easier to find. Visible-light laser <b>110</b> sends visible light into beam launch <b>150</b>, which comprises stable ferrule <b>152</b> and positive lens <b>154</b>. The visible laser beam <b>112</b> that emerges to the beam launch <b>150</b> is collimated. Dichroic beam splitter <b>114</b> transmits ADM beam <b>108</b> but reflects visible beam <b>112</b>. To the right of beam splitter <b>114</b>, composite laser beam <b>116</b> comprises the visible laser beam and ADM laser beam, which are substantially collinear. Laser beam <b>116</b> passes through beam splitter <b>118</b> and beam expander <b>160</b>, emerging as a larger collimated laser beam <b>46</b>. The beam expander comprises negative lens <b>162</b> and positive lens <b>164</b>.

0020The laser beam <b>46</b> travels to external retroreflector <b>26</b>, as shown in <figref idref="DRAWINGS">FIG. 1</figref>. The beam reflects off retroreflector <b>26</b> and returns to the laser tracker. If the laser beam strikes the center of the retroreflector, the reflected laser beam retraces the path of the incident laser beam. If the laser beam strikes the retroreflector off the center, the reflected laser beam returns parallel to the incident beam but offset from it. The returning laser beam re-enters the tracker and retraces the path back through the optical system. Some of the returning laser light reflects off beam splitter <b>118</b>. Reflected laser light <b>126</b> passes through optical filter <b>128</b> and strikes position detector <b>130</b>. The optical filter <b>128</b> blocks either the ADM light or the visible light in the beam <b>126</b>. The position detector <b>130</b> responds to the light that passes through the optical filter <b>128</b> by indicating the position of the laser beam on its surface. The retrace point of the position detector is defined as the point that the laser beam <b>126</b> strikes if the beam <b>46</b> strikes the center of retroreflector <b>26</b>. When the laser beam <b>46</b> moves off the center of retroreflector <b>26</b>, the laser beam <b>126</b> moves off the retrace point and causes the position detector <b>130</b> to generate an electrical error signal. A servo system processes this error signal to activate motors that turn the laser tracker toward the center of the external retroreflector <b>26</b>.

0021The dichroic beam splitter <b>114</b> reflects the returning visible laser beam but transmits the returning ADM laser beam. The returning ADM laser beam travels through the beam launch and is coupled into the optical fiber within the stable ferrule <b>142</b>. This light travels through the fiber-coupling network <b>200</b> and emerges from optical fiber <b>230</b>. That portion of the laser light that traveled through fiber loop <b>106</b> emerges from optical fiber <b>232</b>. Both fibers <b>230</b> and <b>232</b> continue into the ADM electronics section <b>300</b>, where their modulated powers are converted into electrical signals. These signals are processed by the ADM electronics to provide the result, which is the distance from the tracker to the retroreflector target.

0000Fiber-coupling Network

0022Exemplary fiber-coupling network <b>200</b> of <figref idref="DRAWINGS">FIG. 3</figref> comprises first fiber-optic coupler <b>204</b>, second fiber-optic coupler <b>206</b>, and low-reflection terminations <b>208</b> and <b>210</b>. Light from ADM laser <b>102</b> travels through fiber-optic cable <b>104</b> and enters first fiber-optic coupler <b>204</b>. Fiber-optic coupler <b>204</b> sends 10% of the laser light through fiber-loop <b>106</b> and into optical fiber <b>232</b>, which travels to ADM electronics <b>300</b>. Fiber-optic coupler <b>204</b> sends the other 90% of the laser light through fiber-optic coupler <b>206</b>, which sends half of the laser light to low-reflection termination <b>208</b> and the other half of the laser light to stable ferrule <b>142</b>. Light from stable ferrule <b>142</b> propagates to external retroreflector <b>26</b> and back into ferrule <b>142</b>, as described above. Half of the laser light returning through ferrule <b>142</b> travels back through second fiber-optic coupler <b>206</b>, through fiber-optic cable <b>230</b>, and into ADM electronics <b>300</b>. The other half of the laser light travels through second fiber-coupler <b>206</b>, first fiber-optic coupler <b>204</b>, and into ADM laser <b>102</b>, where it is blocked by an internal Faraday isolator (not shown).

0000ADM Electronics

0023ADM electronics <b>300</b> of <figref idref="DRAWINGS">FIG. 4</figref> comprises frequency reference <b>302</b>, synthesizer <b>304</b>, measure detector <b>306</b>, reference detector <b>308</b>, mixers <b>310</b>, <b>312</b>, amplifiers <b>314</b>, <b>316</b>, <b>318</b>, <b>320</b>, frequency divider <b>324</b>, and analog-to-digital converter (ADC) <b>322</b>. Frequency reference <b>302</b> provides the time base for the ADM and should have low phase noise and low frequency drift. The frequency reference may be an oven-controlled crystal oscillator (OCXO), rubidium oscillator, or any other highly stable frequency reference. Preferably the oscillator frequency should be accurate and stable to within a small fraction of a part per million. The signal from the frequency reference is put into the synthesizer, which generates three signals. The first signal is at frequency f_RFand modulates the optical power of ADM laser <b>102</b>. This type of modulation is called intensity modulation (IM). Alternatively, it is possible for the first signal at frequency f_RFto modulate the electric field amplitude, rather than the optical power, of the laser light from ADM laser <b>102</b>. This type of modulation is called amplitude modulation (AM). The second and third signals, both at the frequency f_LO, go to the local-oscillator ports of mixers <b>310</b> and <b>312</b>.

0024Fiber-optic cables <b>230</b> and <b>232</b> carry laser light. The light in these fiber-optic cables is converted into electrical signals by measure detector <b>306</b> and reference detector <b>308</b>. These optical detectors send the modulation frequency f_RFto amplifiers <b>314</b>, <b>316</b> and then to mixers <b>310</b>, <b>312</b>. Each mixer produces two frequencies, one at |f_LO-f_RF| and one at |f_LO+f_RF|. These signals travel to low-frequency amplifiers <b>318</b>, <b>320</b>. These amplifiers block the high-frequency signals so that only the signals at the intermediate frequency (IF), f_IF=|f_LO−f_RF| pass through to the analog-to-digital converter (ADC) <b>322</b>. The frequency reference <b>302</b> sends a signal into frequency divider <b>324</b>, which divides the frequency of the reference <b>302</b> by an integer N to produce a sampling clock. In general, the ADC may decimate the sampled signals by an integer factor M, so that the effective sampling rate is f_REF/NM. This effective sampling rate should be an integer multiple of the intermediate frequency f_IF.

0025Here are frequencies for an exemplary ADM: The frequency reference is f_REF=20 MHz. The synthesizer RF frequency that drives the laser is f_RF=2800 MHz. The synthesizer LO frequency that is applied to the mixers is f_LO=2800.01 MHz. The difference between the LO and RF frequencies is the intermediate frequency of f_IF=10 kHz. The frequency reference is divided by N=10, to produce a 2-MHz frequency that is applied to the ADC as a sampling clock. The ADC has a decimation factor of M=8, which produces an effective sampling rate of 250 kHz. Since the IF is 10 kHz, the ADC takes 25 samples per cycle.

0026The ADC sends the sampled data for the measure and reference channels to data processors <b>400</b> for analysis. Data processors include digital signal processor (DSP) chips and general-purpose microprocessor chips. The processing performed by these processors is described below.

0000Data Processor

0027Data processor <b>400</b> of <figref idref="DRAWINGS">FIG. 5</figref> takes the digitized data from ADC <b>322</b> and derives from it the distance from the tracker to external retroreflector <b>26</b>. <figref idref="DRAWINGS">FIG. 5</figref> refers to this distance as the RESULT. Data processor <b>400</b> comprises digital signal processor <b>410</b>, microprocessor <b>450</b>, and crystal oscillators <b>402</b>, <b>404</b>.

0028Analog-to-digital converter <b>322</b> sends sampled data to DSP <b>410</b>. This data is routed to a program that runs within the DSP. This program contains three main functions: phase-extractor function <b>420</b>, compensator function <b>422</b>, and Kalman-filter function <b>424</b>. The purpose of the phase-extractor function is to determine the phases of the signals in the reference and measure channels, that is, the phases of the signals that pass through the measure detector <b>306</b> and reference detector <b>308</b>. To determine these phases, the modulation range must first be calculated. Modulation range is defined as the round-trip distance traveled by the ADM laser light in air for the phase of the laser modulation to change by 2 pi radians. The modulation range R_MODis given by <br /><i>R</i>_MOD<i>=c/</i>(2 <i>n f</i>_RF),  (1)<br /> where c is the speed of light in vacuum, n is the group index of refraction of the ADM laser light in air, and f_RFis the RF frequency generated by synthesizer <b>304</b> and applied to ADM laser <b>102</b>. In an exemplary ADM having an RF frequency of 2860 MHz, the modulation range is approximately 52 millimeters.

0029As discussed previously, the sample clock applied to ADC <b>322</b> has an effective frequency Of f_SAMP=f_REFNM and the number of ADC samples per cycle is V=f_SAMPf_IF. In an exemplary tracker, f_REF=20 MHz, N=10, M=8, and f_IF=10 kHz. The sample frequency is then 250 kHz and the number of ADC samples per cycle is N_ADC=25 samples per cycle.

0030Let x_kbe the k^thsampled data value from the ADC for the measure channel and let v be the corresponding speed of external retroreflector <b>26</b> during the measurement. Phase-extractor function <b>420</b> calculates the phase p_Mof the measure channel for moving external retroreflector <b>26</b> as follows:

0031<maths id="MATH-US-00001" num="00001"><math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><mi>a</mi><mo>=</mo><mrow><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>V</mi><mo>-</mo><mn>1</mn></mrow></munderover><mo>⁢</mo><mrow><msub><mi>x</mi><mi>k</mi></msub><mo>⁢</mo><mrow><mi>sin</mi><mo>⁡</mo><mrow><mo>(</mo><mrow><mn>2</mn><mo>⁢</mo><mi>π</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>k</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mfrac><mrow><msub><mi>f</mi><mi>IF</mi></msub><mo>-</mo><mrow><mi>v</mi><mo>/</mo><msub><mi>R</mi><mi>MOD</mi></msub></mrow></mrow><msub><mi>f</mi><mi>SAMP</mi></msub></mfrac></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mrow><mo>,</mo></mrow></mtd><mtd><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mi>b</mi><mo>=</mo><mrow><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>V</mi><mo>-</mo><mn>1</mn></mrow></munderover><mo>⁢</mo><mrow><msub><mi>x</mi><mi>k</mi></msub><mo>⁢</mo><mrow><mi>cos</mi><mo>⁡</mo><mrow><mo>(</mo><mrow><mn>2</mn><mo>⁢</mo><mi>π</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>k</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mfrac><mrow><msub><mi>f</mi><mi>IF</mi></msub><mo>-</mo><mrow><mi>v</mi><mo>/</mo><msub><mi>R</mi><mi>MOD</mi></msub></mrow></mrow><msub><mi>f</mi><mi>SAMP</mi></msub></mfrac></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mrow><mo>,</mo></mrow></mtd><mtd><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>p</mi><mi>M</mi></msub><mo>=</mo><mrow><mrow><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>⁡</mo><mrow><mo>(</mo><mrow><mi>a</mi><mo>/</mo><mi>b</mi></mrow><mo>)</mo></mrow></mrow><mo>.</mo></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></mtd></mtr></mtable></math></maths><br /> Let y_kbe the k^thsampled data values from the ADC for the reference channel. Phase-extractor function <b>420</b> calculates the phase p_Rof the reference channel for moving external retroreflector <b>26</b> as follows:

0032<maths id="MATH-US-00002" num="00002"><math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><mi>g</mi><mo>=</mo><mrow><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>V</mi><mo>-</mo><mn>1</mn></mrow></munderover><mo>⁢</mo><mrow><msub><mi>y</mi><mi>k</mi></msub><mo>⁢</mo><mrow><mi>sin</mi><mo>⁡</mo><mrow><mo>(</mo><mrow><mn>2</mn><mo>⁢</mo><mi>π</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>k</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mfrac><msub><mi>f</mi><mi>IF</mi></msub><msub><mi>f</mi><mi>SAMP</mi></msub></mfrac></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mrow><mo>,</mo></mrow></mtd><mtd><mrow><mo>(</mo><mn>5</mn><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mi>h</mi><mo>=</mo><mrow><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>V</mi><mo>-</mo><mn>1</mn></mrow></munderover><mo>⁢</mo><mrow><msub><mi>y</mi><mi>k</mi></msub><mo>⁢</mo><mrow><mi>cos</mi><mo>⁡</mo><mrow><mo>(</mo><mrow><mn>2</mn><mo>⁢</mo><mi>π</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>k</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mfrac><msub><mi>f</mi><mi>IF</mi></msub><msub><mi>f</mi><mi>SAMP</mi></msub></mfrac></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mrow><mo>,</mo></mrow></mtd><mtd><mrow><mo>(</mo><mn>6</mn><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>p</mi><mi>R</mi></msub><mo>=</mo><mrow><mrow><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>⁡</mo><mrow><mo>(</mo><mrow><mi>g</mi><mo>/</mo><mi>h</mi></mrow><mo>)</mo></mrow></mrow><mo>.</mo></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>7</mn><mo>)</mo></mrow></mtd></mtr></mtable></math></maths>

0033Significantly, the phase-extractor function <b>420</b> is dependent on the speed or velocity v, for example the radial speed, of the target as show in equation (2), (3), (5), and (6). The phase-extractor function <b>420</b> also delivers the measure phase p_Mand the reference phase p_Rto the compensator function, which uses these phases to calculate a distance value: <br /><i>d=d</i>₀<i>+R</i>_MOD<i>[W</i>+(<i>p</i>_M<i>−p</i>_R)/2π].  (8)<br /> The quantity W is an integer that accounts for the number of whole modulation intervals to the target. The method for finding this integer is discussed below. In some systems, there may be additional systematic errors that can be removed by appending additional terms to equation (8). For example, some systems experience an error that varies with distance as a sinusoid with a period equal to the modulation range R_MOD. To remove this type of error, it is necessary to use the ADM to measure targets at accurately known distances and observe the sinusoidal error pattern.

0034The compensator <b>422</b> sends the distance values to Kalman filter <b>424</b>. The Kalman filter is a numerical algorithm applied to the distance data to give the best estimate of distance and speed of external retroreflector <b>26</b> as a function of time and in the presence of noise. The ADM distance data is collected at high speed and has some level of random noise in the distance readings. This small error is greatly amplified in calculating speed, since small differences in distance are divided by a small increment in time. The Kalman filter can be thought of as an intelligent smoothing function that optimizes accuracy based on the noise of the system and the speed of the target.

0035The Kalman filter also serves to synchronize the ADM readings with the readings of the angular encoders and the position detector. The angular encoders and position detector latch their readings whenever they receive the sync pulse, which occurs at frequency f_SYNC. The frequency of the sync pulse is in general different than the frequency of calculation of the ADM. In an exemplary tracker, the ADM calculates at a rate of f_IF=10 kHz, while the sync pulse has a frequency of 1.024 kHz. The Kalman filter provides synchronization of the ADM with the angular encoders and position detector by extrapolating the position forward in time to the next sync pulse.

0036There are five general equations that govern the behavior of the Kalman filter. In general, the quantities in these equations are represented by matrices, whose dimensions are determined by the complexity of the implementation of the Kalman filter. The five general equations are <br />x_m=Φx_p,  (9)<br /><i>P</i>_m<i>=ΦP</i>_pΦ^T<i>+Q,</i>  (10)<br /><i>K=P</i>_m<i>H</i>^T(<i>HP</i>_m<i>H</i>^T<i>+R</i>)⁻¹,  (11)<br /><i>x</i>_p<i>=x</i>_m<i>+K</i>(<i>z−Hx</i>_m),  (12)<br /><i>P</i>_p=(<i>P</i>_m⁻¹<i>+H</i>^T<i>R</i>⁻¹<i>H</i>)⁻.  (13)

0037In these equations, the subscript m represents an a priori estimate and the subscript p represents an a posteriori estimate. The quantity x is the state variable that may take a variety of forms. Because the exemplary ADM system measures at a high rate, a relatively simple state vector containing only two components—the position d and radial speed v—are needed:

0038<maths id="MATH-US-00003" num="00003"><math overflow="scroll"><mtable><mtr><mtd><mrow><mi>x</mi><mo>=</mo><mrow><mrow><mo>(</mo><mtable><mtr><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mi>v</mi></mtd></mtr></mtable><mo>)</mo></mrow><mo>.</mo></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>14</mn><mo>)</mo></mrow></mtd></mtr></mtable></math></maths><br /> The corresponding time propagation matrix, assuming unit time steps, is

0039<maths id="MATH-US-00004" num="00004"><math overflow="scroll"><mtable><mtr><mtd><mrow><mi>Φ</mi><mo>=</mo><mrow><mrow><mo>(</mo><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable><mo>)</mo></mrow><mo>.</mo></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>15</mn><mo>)</mo></mrow></mtd></mtr></mtable></math></maths><br /> Equation (9) then corresponds to the equations d_m=d_p+v_p, which means that the estimated distance at the present point in time (d_m) is equal to the estimated distance at the last point in time (d_p) times the estimated speed at the last point in time (v_p) times the time interval between the current and last points in time, which is assumed to equal one. The matrix Q is the process noise covariance. In the simple Kalman filter employed here, the acceleration is not explicitly calculated. Instead the acceleration is assumed to have a dispersion characterized by the variance σ_A². The process-noise variance σ_A²is selected so as to minimize the error in the position of a moving target. The resulting covariance for the process noise is

0040<maths id="MATH-US-00005" num="00005"><math overflow="scroll"><mtable><mtr><mtd><mrow><mi>Q</mi><mo>=</mo><mrow><mrow><msubsup><mi>σ</mi><mi>A</mi><mn>2</mn></msubsup><mo>⁡</mo><mrow><mo>(</mo><mtable><mtr><mtd><mrow><mn>1</mn><mo>/</mo><mn>4</mn></mrow></mtd><mtd><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></mtd><mtd><mn>1</mn></mtd></mtr></mtable><mo>)</mo></mrow></mrow><mo>.</mo></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>16</mn><mo>)</mo></mrow></mtd></mtr></mtable></math></maths><br /> P_mis the state covariance matrix at the present point in time. It is found from the state covariance matrix at the last point in time and the process noise covariance. The state covariance matrix and the measurement noise covariance R are used to determine the filter gain K. In the simple case considered here, the measurement noise covariance is just the variance σ_M²in readings caused by noise in the measurement device. In this case, the measurement noise in the ADM system is determined by simply calculating the variance σ_ADM²in the distances reported while the ADM is measuring a stationary target. H is the measurement matrix, which is defined such that H times the state estimate x is equal to the estimated output, against which measured output, is compared. In the case considered here the measurements are of the distance d and so H=(1 0).

0041Equation (12) is interpreted as follows. x_mis the initial guess for the state vector (distance and radial speed) based on the distance and radial speed for the previous point in time. The quantity z is the measured distance d and Hx_mis the estimated distance. The quantity z−Hx_mis the difference between the measured and estimated distances. This difference is multiplied by the gain matrix K to provide an adjustment to the initial estimate x_mfor the state matrix. In other words, the best estimate for the distance is a value between the measured distance and the estimated distance. Equation (12) provides a mathematically sound method of selecting the best (a posteriori) estimate of the distance and radial speed. Equation (13) provides a new estimate for the state covariance P_pat the next point in time. Equations (9)-(13) are solved each time compensator function <b>422</b> sends a new measured value to the Kalman filter.

0042To synchronize the ADM measurement to the measurements of the angular encoders and position detector, counter <b>414</b> determines the difference in time between the sync pulse and the last state distance. It does this in the following way. Crystal oscillator <b>404</b> sends a low-frequency sine wave to frequency divider <b>452</b>, located within microprocessor <b>450</b>. This clock frequency is divided down to f_SYNC, the frequency of the sync pulse. The sync pulse is sent over device bus <b>72</b> to DSP <b>410</b>, angular encoder electronics <b>74</b>, and position-detector electronics <b>76</b>. In an exemplary system, the oscillator sends a 32.768 kHz signal through frequency divider <b>452</b>, which divides by 32 to produce a sync-pulse frequency f_SYNC=1.024 kHz. The sync pulse is sent to counter <b>414</b>, which resides within DSP <b>410</b>. The counter is clocked by crystal <b>402</b>, which drives a phase-locked loop (PLL) device <b>412</b> within the DSP. In the exemplary system, oscillator <b>402</b> has a frequency of 30 MHz and PLL <b>412</b> doubles this to produce a clock signal of 60 MHz to counter <b>414</b>. The counter <b>414</b> determines the arrival of the sync pulse to a resolution of 1/60 MHz =16.7 nanoseconds. The phase-extractor function <b>420</b> sends a signal to the counter when the ADC <b>322</b> has sent all the samples for one cycle. This resets counter <b>414</b> and begins a new count. The sync pulse stops the counting of counter <b>412</b>. The total number of counts is divided by the frequency to determine the elapsed time. Since the time interval in the above equations was set to one, the normalized time interval t_NORMis the elapsed time divided by the time interval. The state distance x_EXTextrapolated to the sync pulse event is <br /><i>x</i>_EXT<i>=x</i>_k<i>+v</i>_k<i>t</i>_NORM.  (17)<br /> The Kalman-filter function <b>424</b> provides the result, which is the distance from the tracker to external retroreflector <b>26</b>. The Kalman filter also provides the velocity to phase-extractor function <b>420</b> to apply in equations (2), (3), (5), and (6).

0043Previously the quantity W was introduced in equation (8) as an integer that accounts for the number of whole modulation intervals to the target. This integer value W is found by first measuring the distance to the external retroreflector <b>26</b>. The frequencies f_RFand f_LOare changed by a fixed amount and the distances are again measured. If the RF frequencies before and after the change are f₁and f₂and the phase difference between the two measurements is p then the integer W is equal to the integer portion of (p/2π)(f₁/|f₂−f₁|). This technique will work out to a range of (c/2n)/(f₂−f₁). For example, if f₁and f₂differ by 2.5 MHz, and if they f₁is 2800 MHz, then the technique will work out to about 60 meters. If desired, a third frequency can be added to assist in determining the value of the integer W. Once W has been determined, it is not necessary to switch the frequencies again unless the beam is broken. If the ADM continues to measure the external retroreflector <b>26</b> without interruption, then it can easily keep track of the changes in the integer W.

0044It will be apparent to those skilled in the art that, while exemplary embodiments have been shown and described, various modifications and variations can be made to the apparatus and method of measuring a moving retroreflector with an absolute distance meter disclosed herein without departing from the spirit or scope of the invention. Accordingly, it is to be understood that the various embodiments have been described by way of illustration and not limitation.